Minimum Stirrups and the Section-Size Limit (ACI 318-19 9.6.3)
The detailing checks that sit beside the rc-beam-shear strength math, and the one a beam can pass strength yet fail: ACI 318-19 9.6.3.4 Av,min/s = greater of 0.75 sqrt(f'c) bw/fyt and 50 bw/fyt (the 50 bw/fyt floor governs below about 4,444 psi), the 9.6.3.1 trigger Vu > phi lambda sqrt(f'c) bw d that the 2019 edition put in place of the old 0.5 phi Vc rule, the 22.5.1.2 ceiling Vs <= 8 sqrt(f'c) bw d, and the 9.7.6.2.2 spacing cap of d/2 and 24 in, halved past Vs = 4 sqrt(f'c) bw d. A 12 x 21.5 in beam with #3 stirrups needs Av/s = 0.0100 in^2/in, so 22 in satisfies the minimum but the d/2 = 10.75 in cap governs; the section itself tops out at 122.4 kip no matter how much steel goes in. Table 9.6.3.1 exemptions not modeled. A design aid, not the engineer of record's stamped design.
Formula and source
Av,min/s = max(0.75 sqrt(f'c) bw/fyt, 50 bw/fyt); s(Av,min) = Av / (Av,min/s); trigger = phi lambda sqrt(f'c) bw d; Vs,max = 8 sqrt(f'c) bw d; phi Vn,max = phi (2 lambda sqrt(f'c) bw d + Vs,max); s <= min(d/2, 24 in), or min(d/4, 12 in) when Vs > 4 sqrt(f'c) bw d. (phi = 0.75)
The ACI 318-19 9.6.3.4 minimum shear reinforcement, the 9.6.3.1 Av,min trigger, the 22.5.1.2 Vs section-size ceiling, and the 9.7.6.2.2 stirrup-spacing maxima, by name.
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